How to Calculate Tan Inverse in Excel in Degrees
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The inverse tangent function (tan⁻¹) calculates the angle whose tangent is a given value. In Excel, you can calculate this in degrees using the ATAN2 function combined with degree conversion. This guide explains how to do it accurately and provides a built-in calculator for quick reference.
What is Tan Inverse?
The inverse tangent function, often written as tan⁻¹(y/x) or arctan(y/x), calculates the angle θ in a right triangle where the tangent of θ is equal to the ratio of the opposite side (y) to the adjacent side (x).
In Excel, the ATAN2 function calculates this angle in radians. To get the result in degrees, you need to multiply by 180/π (approximately 57.2958).
Excel Formula for Tan Inverse
Formula
=DEGREES(ATAN2(opposite, adjacent))
Where:
oppositeis the length of the side opposite the angleadjacentis the length of the side adjacent to the angle
This formula first calculates the angle in radians using ATAN2, then converts it to degrees using the DEGREES function.
Step-by-Step Guide
- Open your Excel spreadsheet and enter the values for the opposite and adjacent sides of the angle you want to calculate.
- In an empty cell, type
=ATAN2(. - Click the cell containing the opposite side value, type a comma, then click the cell containing the adjacent side value.
- Type
)to complete the ATAN2 function. - Type
*180/PI()to convert the result from radians to degrees. - Press Enter to display the angle in degrees.
Alternative Formula
You can also use the combined formula: =DEGREES(ATAN2(opposite, adjacent)) which is more concise and directly converts to degrees.
Common Mistakes to Avoid
- Using ATAN instead of ATAN2: ATAN only takes one argument and doesn't handle the quadrant correctly.
- Forgetting to convert from radians to degrees: Excel's trigonometric functions return results in radians by default.
- Entering negative values incorrectly: ATAN2 properly handles all quadrants when given both x and y coordinates.
Practical Examples
| Opposite Side | Adjacent Side | Angle (Degrees) |
|---|---|---|
| 3 | 4 | 36.87° |
| 5 | 5 | 45.00° |
| 1 | √3 | 30.00° |
These examples show how the angle changes based on the ratio of the opposite to adjacent sides.
Frequently Asked Questions
- Can I use ATAN instead of ATAN2?
- No, ATAN only takes one argument and doesn't properly handle the quadrant of the result. ATAN2 is the correct function for calculating angles in all quadrants.
- Why do I need to multiply by 180/π?
- Excel's trigonometric functions return results in radians by default. Multiplying by 180/π converts the result to degrees.
- What if my adjacent side is zero?
- If the adjacent side is zero, the angle is 90 degrees (π/2 radians). The formula will still work correctly in this case.
- Can I use this formula for 3D coordinates?
- Yes, ATAN2 can be used with 3D coordinates by calculating the angle in the x-y plane. For spherical coordinates, you would need additional calculations.